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Transactions of the American Mathematical Society

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The $p$-adic log gamma function and $p$-adic Euler constants


Author: Jack Diamond
Journal: Trans. Amer. Math. Soc. 233 (1977), 321-337
MSC: Primary 12B40; Secondary 33A15
DOI: https://doi.org/10.1090/S0002-9947-1977-0498503-9
MathSciNet review: 0498503
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Abstract: We define ${G_p}$, a p-adic analog of the classical log gamma function and show it satisfies relations similar to the standard formulas for log gamma. We also define p-adic Euler constants and use them to obtain results on $G{’_p}$ and on the logarithmic derivative of Morita’s ${\Gamma _p}$.


References [Enhancements On Off] (What's this?)

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Keywords: Log gamma function, Euler constants, <I>p</I>-adic functions
Article copyright: © Copyright 1977 American Mathematical Society